THE GIRL WITH THE ‘X-RAY EYES!
There is a BBC TV programme, “Horizon”, that deals with scientific subjects in a serious way.
One of these was about a Russian girl who claimed to have ‘x-ray vision’. She said that she could look inside a patient’s body and see what was wrong with him/her.
In and around her home town she was famed. She had astounded doctors by diagnosing conditions that they had missed.
Her story reached
Two tests were set up. The first was where she decided on the conditions, and the second where the specialists set out the test conditions.
The first test went very well.
The second test was judged a failure.
This test arranged for seven people to be examined. Six had various conditions, and one had no known problems.
The girl was then given seven cards, on which were written the conditions of the seven people. Her task was to put the correct card against the person.
She took a very long time to do this, and got four correct. The experts said that five out of seven would be due to chance.
I accepted this, but later, mulling it over, the chance odds seemed to be high.
I took some playing cards, Ace to Seven of Hearts, and Ace to Seven of Spades. The hearts were the patients, and the spades were the cards with the correct diagnoses. I shuffled the hearts, and placed them face down on the table. Then, I took the spades, looked at them, and tried to guess the correct placing. Having done this for about a dozen tries, I found that I was only getting one, and rarely two correct! The odds used by the ‘experts’ seemed way out.
Not being a statistician I used my logic and wrote a simple program to test the results over thousands of tries.
The results confirmed my suspicions. The average over several 10,000 tries was 0.9976, or one correct per attempt.
This leaves the question of whether the girl really did diagnose the conditions with a significantly higher accuracy than chance.
The notes on the program are next. You can run the program, and see the results. Let me know if you get a higher average score than one.